Quantile based estimation of biasing parameters in ridge regression model

Abstract

Ridge regression is used to get precise estimates by introducing some bias when the problem of multicollinearity is present in the model. Biasing parameter plays a vital role in this bias-variance tradeoff. Several methods are available in literature for the estimation of biasing parameter. For high noise and multicollinearity, available methods do not perform well in terms of their mean square error. In this article, we proposed a new estimator and compared its performance with some other available estimators. Our suggested estimator is a class of estimators based on quantile of ratio of error variance to the canonical coefficients. Based on simulation study, our proposed estimator outperforms other estimators especially when multicollinearity and error variance are high. Finally, a real-life example is used to illustrate the application of the proposed estimator.